Whakaoti i te ∫ x(2+x^2)^2 wrt x

$$\int x ( 2 + x ^ { 2 } ) ^ { 2 } d x$$

Aromātai

$$\frac{x^{6}}{6}+x^{4}+2x^{2}+С$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(2+x^{2}\right)^{2}.

$$\int x\left(4+4x^{2}+\left(x^{2}\right)^{2}\right)\mathrm{d}x$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 2 me te 2 kia riro ai te 4.

$$\int x\left(4+4x^{2}+x^{4}\right)\mathrm{d}x$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 4+4x^{2}+x^{4}.

$$\int 4x+4x^{3}+x^{5}\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 4x\mathrm{d}x+\int 4x^{3}\mathrm{d}x+\int x^{5}\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$4\int x\mathrm{d}x+4\int x^{3}\mathrm{d}x+\int x^{5}\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x\mathrm{d}x ki te \frac{x^{2}}{2}. Whakareatia 4 ki te \frac{x^{2}}{2}.

$$2x^{2}+4\int x^{3}\mathrm{d}x+\int x^{5}\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{3}\mathrm{d}x ki te \frac{x^{4}}{4}. Whakareatia 4 ki te \frac{x^{4}}{4}.

$$2x^{2}+x^{4}+\int x^{5}\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{5}\mathrm{d}x ki te \frac{x^{6}}{6}.

$$2x^{2}+x^{4}+\frac{x^{6}}{6}$$

Mēnā ko F\left(x\right) he pārōnaki kōaro o f\left(x\right), kāti ko te huinga o ngā pārōnaki kōaro katoa o f\left(x\right) ka whakaaturia e F\left(x\right)+C. Nō reira, me tāpiri te pūmau o te whakatōpūtanga C\in \mathrm{R} ki te otinga.

$$\frac{x^{6}}{6}+x^{4}+2x^{2}+С$$

Kimi Pārōnaki e ai ki x

$$x\left(x^{2}+2\right)^{2}$$